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29% (01:51) correct
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Three problems were given to participants of a math contest. Each participant got 0, 1, 2, or 3 points for each problem. After the papers were graded it turned out that no pair of participants received matching scores for more than one problem. What is the largest possible number of participants?
A. 8
B. 9
C. 12
D. 16
E. 24
Are You Up For the Challenge: 700 Level Questions
A. 8
B. 9
C. 12
D. 16
E. 24
Are You Up For the Challenge: 700 Level Questions
03 Oct 2022, 07:11
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Bunuel
You want to maximize the number of pairings within the constraint in order to maximize the number of participants.
If you had 2 questions with 2 answers and 2 participants you could assign both participants to answer 1 of question 1 and still be able to assign them separate answers for question 2.
With 3 participants you assign the 3rd participant answer 2 of question 1 and either answer for question 2 without a problem.
A similar approach works for a 4th participant, with 2 distinct participants being paired for each answer.
Since a pair of participants, say answer 1, has to be split between the two answers for question 2, a 5th participant would unavoidably be paired a second time with two of the four for the second question, violating the constraint.
So the maximum number of participants that can appear per answer has to be no more than the number of answers per question, since they need to be split among those answers subsequently.
So, for 4 answers per question, that would mean no more than 4 individuals per answer, limiting the total to
16
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